15 research outputs found
Mode-Locking in Driven Disordered Systems as a Boundary-Value Problem
We study mode-locking in disordered media as a boundary-value problem.
Focusing on the simplest class of mode-locking models which consists of a
single driven overdamped degree-of-freedom, we develop an analytical method to
obtain the shape of the Arnol'd tongues in the regime of low ac-driving
amplitude or high ac-driving frequency. The method is exact for a scalloped
pinning potential and easily adapted to other pinning potentials. It is
complementary to the analysis based on the well-known Shapiro's argument that
holds in the perturbative regime of large driving amplitudes or low driving
frequency, where the effect of pinning is weak.Comment: 6 pages, 7 figures, RevTeX, Submitte
Influence of typical environments on quantum processes
We present the results of studying the influence of different environmental
states on the coherence of quantum processes. We choose to discuss a simple
model which describe two electronic reservoirs connected through tunneling via
a resonant state. The model could, e.g., serve as an idealization of inelastic
resonant tunneling through a double barrier structure. We develop Schwinger's
closed time path formulation of non-equilibrium quantum statistical mechanics,
and show that the influence of the environment on a coherent quantum process
can be described by the value of a generating functional at a specific force
value, thereby allowing for a unified discussion of destruction of phase
coherence by various environmental states: thermal state, classical noise, time
dependent classical field, and a coherent state. The model allows an extensive
discussion of the influence of dissipation on the coherent quantum process, and
expressions for the transmission coefficient are obtained in the possible
limits.Comment: 46 pages, 11 post script figures. Accepted for publication in
Physical Review
Lubricating Bacteria Model for Branching growth of Bacterial Colonies
Various bacterial strains (e.g. strains belonging to the genera Bacillus,
Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns
during growth on poor semi-solid substrates. These patterns reflect the
bacterial cooperative self-organization. Central part of the cooperation is the
collective formation of lubricant on top of the agar which enables the bacteria
to swim. Hence it provides the colony means to advance towards the food. One
method of modeling the colonial development is via coupled reaction-diffusion
equations which describe the time evolution of the bacterial density and the
concentrations of the relevant chemical fields. This idea has been pursued by a
number of groups. Here we present an additional model which specifically
includes an evolution equation for the lubricant excreted by the bacteria. We
show that when the diffusion of the fluid is governed by nonlinear diffusion
coefficient branching patterns evolves. We study the effect of the rates of
emission and decomposition of the lubricant fluid on the observed patterns. The
results are compared with experimental observations. We also include fields of
chemotactic agents and food chemotaxis and conclude that these features are
needed in order to explain the observations.Comment: 1 latex file, 16 jpeg files, submitted to Phys. Rev.
Stacking Interactions in Denaturation of DNA Fragments
A mesoscopic model for heterogeneous DNA denaturation is developed in the
framework of the path integral formalism. The base pair stretchings are treated
as one-dimensional, time dependent paths contributing to the partition
function. The size of the paths ensemble, which measures the degree of
cooperativity of the system, is computed versus temperature consistently with
the model potential physical requirements. It is shown that the ensemble size
strongly varies with the molecule backbone stiffness providing a quantitative
relation between stacking and features of the melting transition. The latter is
an overall smooth crossover which begins from the \emph{adenine-thymine} rich
portions of the fragment. The harmonic stacking coupling shifts, along the
-axis, the occurrence of the multistep denaturation but it does not change
the character of the crossover. The methods to compute the fractions of open
base pairs versus temperature are discussed: by averaging the base pair
displacements over the path ensemble we find that such fractions signal the
multisteps of the transition in good agreement with the indications provided by
the specific heat plots.Comment: European Physical Journal E (2011) in pres
Graphical and numerical representations of DNA sequences: statistical aspects of similarity
Resonance and mode conversion of phonons scattered by superlattices with inhomogeneity
Scaling behavior of nucleotide cluster in DNA sequences
In this paper we study the scaling behavior of nucleotide cluster in 11 chromosomes of Encephalitozoon cuniculi Genome. The statistical distribution of nucleotide clusters for 11 chromosomes is characterized by the scaling behavior of P(S)∝e(−αS), where S represents nucleotide cluster size. The cluster-size distribution P(S (1)+S (2)) with the total size of sequential C-G cluster and A-T cluster S (1)+S (2) were also studied. P(S (1)+S (2)) follows exponential decay. There does not exist the case of large C-G cluster following large A-T cluster or large A-T cluster following large C-G cluster. We also discuss the relatively random walk length function L(n) and the local compositional complexity of nucleotide sequences based on a new model. These investigations may provide some insight into nucleotide cluster of DNA sequence